On a hot summer night, the refractive index of air is smallest near the ground and increases with height from the ground. When a light beam is directed horizontally, the Huygens' principle leads us to conclude that as it travels, the light beam :

Assuming human pupil to have a radius of $$0.25$$ $$cm$$ and a comfortable viewing distance of $$25$$ $$cm$$, the minimum separation between two objects that human eye can resolve at $$500$$ $$nm$$ wavelength is :

An $$LCR$$ circuit is equivalent to a damped pendulum. In an $$LCR$$ circuit the capacitor is charged to $${Q_0}$$ and then connected to the $$L$$ and $$R$$ as shown below :

If a student plots graphs of the square of maximum charge $$\left( {Q_{Max}^2} \right)$$ on the capacitor with time$$(t)$$ for two different values $${L_1}$$ and $${L_2}$$ $$\left( {{L_1} > {L_2}} \right)$$ of $$L$$ then which of the following represents this graph correctly ?
$$\left( {plots\,\,are\,\,schematic\,\,and\,\,niot\,\,drawn\,\,to\,\,scale} \right)$$

An inductor $$(L=0.03$$ $$H)$$ and a resistor $$\left( {R = 0.15\,k\Omega } \right)$$ are connected in series to a battery of $$15V$$ $$EMF$$ in a circuit shown below. The key $${K_1}$$ has been kept closed for a long time. Then at $$t=0$$, $${K_1}$$ is opened and key $${K_2}$$ is closed simultaneously. At $$t=1$$ $$ms,$$ the current in the circuit will be : $$\left( {{e^5} \cong 150} \right)$$